== http://arxiv.org/abs/1004.1780 == III. TRANSITION AMPLITUDES In a general covariant quantum theory, the dynamics can be given by associating an amplitude to each boundary state [32, 33]. Therefore, the dynamics is given by a linear functional W on H. The modulus square P(ψ) = |⟨W|ψ⟩|2 is the probability associated to the process deﬁned by the boundary state ψ. This is described in detail, for instance, in the book . How is W deﬁned? As pointed out by Eugenio Bianchi in his Nice lectures , the form of W is largely determined by general principles: Feynman’s superposition principle, locality, diﬀeomorphism invariance, crossing symmetry, and local Lorentz invariance. ... ==endquote== If you'd like to examine this in context, it is on page 7 of the paper. One thing we could do in this thread is to think about each of these general principles and the heuristic way that the quantum gravity transition amplitudes arise from them.